Roman numeral calculator
XLVII × XIX = DCCCXCIII in the Roman numeral calculator: 47 × 19 = 893, written back as 500 + 300 + 90 + 3.
The product
- In digits
- 47 × 19 = 893
- First numeral
- XLVII = 47
- Second numeral
- XIX = 19
- How DCCCXCIII is built
- D (500) + C (100) + C (100) + C (100) + XC (90) + I (1) + I (1) + I (1) = 893
- Each numeral is read as a number, the arithmetic is done in digits, and the answer is written back in numerals.
How the Roman Numeral Converter works
Arithmetic with Roman numerals goes through ordinary numbers: read each numeral as a number, do the sum, and write the answer back as a numeral. The Romans worked the same way, calculating on a counting board or an abacus and using the numerals only to record the result.
To read a numeral, add its symbols from left to right and subtract any symbol that stands before a larger one. XLVII is XL (40) + V (5) + II (2) = 47, and XIX is X (10) + IX (9) = 19.
To write the answer, take the largest value that fits, write its symbol, subtract and repeat, treating the pairs CM, CD, XC, XL, IX and IV as values of their own. 47 × 19 = 893 is D (500), then CCC (300), then XC (90), then III (3): DCCCXCIII.
Addition can also be done inside the numerals. Expand the subtractive pairs, pool the symbols and regroup: five Is make a V, two Vs an X, five Xs an L, two Ls a C, five Cs a D and two Ds an M. MCMXCIV + XXXII expands to M DCCCC LXXXX IIII + XXXII, and regrouping the pile settles at MMXXVI, 2,026. Subtraction runs the other way, breaking a large symbol into smaller ones to borrow, the way 2,026 - 1,994 = 32 needs one M broken into hundreds.
Division gives a whole quotient and a remainder: C ÷ VII is XIV remainder II, because 14 × 7 + 2 = 100. Roman fractions existed, in twelfths called unciae, but they were a separate system used for money and measures.
There are limits on both sides. With no zero, X - X has no numeral, and nothing below 1 can be written. Standard notation stops at 3,999, so MMM × II = 6,000 needs digits, or a bar over the numeral, the vinculum, which multiplies it by 1,000.
Roman Numeral Converter FAQ
How do you add Roman numerals?
Convert each to a number, add, and convert back: XXIV + XVIII is 24 + 18 = 42, which is XLII. Or work in the symbols: XXIV + XVIII expands to XXIIII + XVIII and pools to XXX V IIIIIII. Seven Is are a V and II, two Vs are an X, and XXXXII is written XLII.
How do you multiply Roman numerals?
Multiply the values and write the product back as a numeral. XII × XII is 12 × 12 = 144, which is C (100) + XL (40) + IV (4), so CXLIV.
What is MMXXVI minus MCMXCIV?
XXXII. MMXXVI is 2,026 and MCMXCIV is 1,994, so the difference is 32, written XXX (30) and II (2).